Integration: the Area Problem
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The formula to find areas underneath curves derived from scratch
by
Tiago Hands
Key Questions

Let us look at the definition of a definite integral below.
Definite Integral
#\int_a^b f(x) dx=lim_{n to infty}sum_{i=1}^n f(a+iDelta x)Delta x# ,
where#Delta x ={ba}/n# .If
#f(x)ge0# , then the definition essentially is the limit of the sum of the areas of approximating rectangles, so, by design, the definite integral represents the area of the region under the graph of#f(x)# above the xaxis. 
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Videos on topic View all (8)
Introduction to Integration

1Sigma Notation

2Integration: the Area Problem

3Formal Definition of the Definite Integral

4Definite and indefinite integrals

5Integrals of Polynomial functions

6Determining Basic Rates of Change Using Integrals

7Integrals of Trigonometric Functions

8Integrals of Exponential Functions

9Integrals of Rational Functions

10The Fundamental Theorem of Calculus

11Basic Properties of Definite Integrals